On Local Algebras of Maximal Algebras of Jordan Quotients

2020 ◽  
pp. 49-59
Author(s):  
F. Montaner ◽  
I. Paniello
Keyword(s):  
Local Algebras

Applications of Local Algebras of Differentiable Manifolds

2015 ◽  
Vol 207 (3) ◽  
pp. 485-511 ◽  
Author(s):  
M. Jukl ◽  
L. Juklová ◽  
J. Mikeš
Keyword(s):  
Differentiable Manifolds ◽  
Local Algebras

Symmetric local algebras

1990 ◽  
pp. 203-251
Author(s):  
Gregory Karpilovsky
Keyword(s):  
Local Algebras

SYMMETRIES IN THEORY OF LOCAL OBSERVABLES AND THE CHOICE OF THE NET OF LOCAL ALGEBRAS

1992 ◽  
Vol 04 (spec01) ◽  
pp. 1-14 ◽  
Author(s):  
HUZIHIRO ARAKI
Keyword(s):  
Scattering Theory ◽  
Local Observable ◽  
Particle Spectrum ◽  
Massive Scalar ◽  
Local Algebras ◽  
Local Observables ◽  
Physical Consequences ◽  
Sector Theory ◽  
Internal Symmetries

For a given net of algebras of local observables, satisfying standard assumptions, we propose the problem of classifying a net of subalgebras which provides the same physical consequences (possibly via Doplicher-Haag-Roberts sector theory) such as particle spectrum and scattering theory. The notion of symmetry of the net of local algebras are introduced and its geometrical aspects are analyzed, with the conclusion that the net reproduces the geometry of supporting regions to some extent. The internal symmetries provides a possible net of subalgebras, as is discussed by Doplicher, Haag and Roberts. We discuss other possibilities by generating subalgebras from a local observable. Results and problems for the simple case of a neutral massive scalar free Held are summarized.

scholarly journals Quantum Markov chains: A unification approach

2020 ◽  
Vol 23 (02) ◽  
pp. 2050016 ◽  
Author(s):  
Luigi Accardi ◽  
Abdessatar Souissi ◽  
El Gheteb Soueidy
Keyword(s):  
Markov Chains ◽  
Algebraic Property ◽  
Markov Property ◽  
Unified Approach ◽  
Local Algebras ◽  
Quantum Markov Chains

In this paper, we study a unified approach for quantum Markov chains (QMCs). A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic algebraic property. We stress that this kind of algebras includes both Boson and Fermi algebras. Our main results concern two reconstruction theorems for quantum Markov chains and for quantum Markov states. Namely, we illustrate the results through examples.

Sign in / Sign up

Export Citation Format

Share Document